Any digital representation of a continuous analog function involves describing the function as a sequence of discrete samples. However, the information to be extracted from the function may reside in attributes or characteristics of the waveform that are lost in the sampling process.
For example, in surveillance and communications systems, there is a need to determine extreme values (minimum or maximum values) in a function and the location of such extrema. However, in discrete or digital processors, only discretely sampled values of the function, not necessarily including such extrema, are available.
A specific example is a pulsed radar, which receives successive echoes, corresponding to a given range, as its antenna beam scans over a target. Usually, the information desired from the echoes is the position of the antenna beam as its maximum sweeps over the target, that is, the position of maximum return. However, the successive echoes from the target are separated in time by the interval between transmitted pulses. Consequently, unless the scanning rate is slow compared to the interval between transmit pulses, there may be no echo at the peak of the beam. Thus, the returned echoes "straddle" the beam maximum, resulting in increased uncertainty in the time at which the beam maximum passed over the target and a possible reduction in the size (amplitude) of the echo.
Similarly, in the processing of a particular sweep or range trace, the echo is sampled at times corresponding to particular ranges. Thus, the resultant range output is quantized in steps corresponding to the particular sampled ranges. Consequently, when sampling times "straddle" the position of the peak of a processed echo there is an error in estimation of the time of occurrence of the peak. Such a situation, in particular, occurs in digital processing of the trace.
Time quantization errors also occur in determining the leading and trailing edges of an extended pulse, e.g., in radar the return from a target whose range extent is larger than the range resolution of the radar system.
Related errors occur in digital communications, in radio direction finding, and radio navigation.
Such time quantization errors may be reduced by interpolating the values of the sampled function during the interval occurring between sampling times. The present invention provides a method and apparatus for performing such interpolations.